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3 years ago

Explain how you know 21/100 is greater than 1/5

1 answer:

5 0

This problem can be solved using equivalent fractions. The first step in resolving this problem is to realize that fractions are best compared when they both have the same denominator. In this case, I will choose to make that common denominator 100. There is no need to rewrite the fraction $\frac{21}{100}$ as the denominator for this fraction is already 100. The fraction $\frac{1}{5} =\frac{20}{100}$ . This is achieved by multiplying both the numerator and denominator by 20. Now that the two fractions have the same denominator, we can easily see that $\frac{21}{100}$ is greater than $\frac{1}{5}$ because it is greater than its equivalent fraction.

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1. Taylor needs to purchase a car. The car Taylor plans to purchase costs $10,000. Taylor has saved $2,000 to use as a down paym

Alexxandr [17]

Answer:

a. The amount Taylor will need to finance is $8,000

b. The amount Taylor pays as interest in one year is $400

Step-by-step explanation:

The given parameters of the financing for the car are;

The cost of the car Taylor plans to purchase, C = $10,000

The amount Taylor has saved to be used as down payment, S = $2,000

The interest rate of the credit Taylor is offered = 5%

The duration given for repayment of the loan = 5 years

a. To purchase the car, the amount Taylor will need to finance, 'P', is given as follows;

P = C - S

∴ P = $10,000 - $2,000 = $8,000

b. The amount of interest on the loan in one year, 'I', is given by the following formula;

$I = \dfrac{P \times R \times T}{100}$

Where;

I = The interest payed

P = The principal amount taken as loan = $8,000

R = The interest rate = 5% APR

T = The time period the interest is applied = 1 year

Plugging in the values, we get;

$I = \dfrac{\$ \, 8,000 \times 5 \times 1}{100} = \$ \, 400$

The interest Taylor will pay on the loan in one year, I = $4,00

7 0

3 years ago

The number of people in a car that crosses a certain bridge is represented by the random variable X, which has a mean value μX =

Alona [7]

Let $Y$ be the total amount of money paid by any given set of passengers. If there are $X$ passengers in a car, then the driver must pay a toll of $Y=0.5X+3$ .

Then $Y$ has first moment (equal to the mean)

$E[Y]=E[0.5X+3]=0.5E[X]+3E[1]=0.5\mu_X+3=\boxed{4.35}$

and second moment

$E[Y^2]=E[0.25X^2+3X+9]=0.25E[X^2]+3E[X]+9E[1]=0.25E[X^2]+3\mu_X+9$

Recall that the variance is the difference between the first two moments:

$\mathrm{Var}[X]=E[X^2]-E[X]^2\implies E[X^2]={\sigma^2}_X+{\mu_X}^2$

$\implies E[Y^2]=0.25({\sigma^2}_X+{\mu_X}^2)+3\mu_X+9\approx19.22$

$\implies\mathrm{Var}[Y]=E[Y^2]-E[Y]^2=\boxed{0.3}$

3 0

3 years ago

Given: ∆AMK, MP ⊥ AK , MP = 10 m∠A = 72º, m∠PMK = 50° Find AM, MK, AK

mina [271]

Answer:

Step-by-step explanation:

The diagram of triangle AMK is shown on the attached photo. To determine AM, we would apply trigonometric ratio since triangle AMP is a right angle triangle.

Sin# = opposite/hypotenuse

Sin 72 = 10/AM

AMSin72 = 10

AM = 10/Sin72 = 10/0.9511

AM = 10.51

To determine MK,

Cos# = adjacent/hypotenuse

Cos 50 = 10/MK

MKCos50 = 10

MK = 10/Cos50 = 10/0.6428

MK = 15.6

AK = AP + KP

Tan# = opposite/adjacent

Tan 72 = 10/AP

AP tan 72 = 10

AP =10/tan72 = 10/ 3.0777 = 3.25

Tan 50 = KP/10

KP = 10tan50

KP= 10× 1.1918 = 11.918

Therefore,

AK = 3.25 + 11.918 = 15.168

3 0

3 years ago

Heeeeeeeeeeeeeeeeelp

malfutka [58]

Answer:

A no-doest pass the vertical line test

Step-by-step explanation:

the vertical line test is a test saying any line is functional if when several vertical lines are drawn, the function does not pass through any line more than once

hope this helps:)!

3 0

3 years ago

Can u guys PLEASE answer this question ASAP. A fat cat that was initially 12 kg reduces its weight by 10% each month. How long d

Mkey [24]

Answer:

It takes at least 7 months for the cat to be at least 6 kg lighter than the original weight.

Step-by-step explanation:

Use exponential decay formula:

A = P (1-r)t

A = amount decreased to

P = original amount

r = rate of decrease

t = time

6 ≥ 12 (1-0.10)t divide both sides by 12

0.5 ≥ (0.9)t take log of both sides

log (0.5) ≥ log (0.9)t power rule of logs lets the exponent t drop to front of log to become a factor

log (0.5) ≥ t log(0.9) divide both sides by log(0.9) which is negative so reverse the inequality sign

log (0.5) / log (0.9) ≤ t use calculator

6.57 ≤ t

It takes at least 7 months for the cat to be at least 6 kg lighter that original weight.

check:

12 (0.9)7≈ 5.73

12 (0.9)6 ≈ 6.37

5 0

3 years ago